Saturday, July 4, 2015

Inverse function and rotation matrix

To understand why graphs of inverse functions are symmetric about the line, try see this from a different point of view: symmetry about is equivalent to symmetry about the x-axis if you rotate the points by , right?

Let’s verify it. Given one arbitrary point in function (mapping) , then is in . Rotate both points by , we have:

Go ahead and see that and differ only in the sign of their x-coordinates!